This activity compares the effects of absolute and relative comparisons on a picture. Think about what would happen to a drawing if every line were made half as long. Would it look like the same picture at all? What would happen if you made every line a half-inch shorter? In this activity, you will see the effects of these changes on Quadperson, a drawing of a face made of quadrilaterals.

(one grid = 1/2 inch)

On a piece of graph paper, draw a picture of Quadperson so that each line in your drawing is half as long as the corresponding line in the picture above. Then, make another picture of Quadperson so that each line in your drawing is a half-inch less in length as the corresponding line in the original Quadperson.

Compare the "before" and "after" quadperson when you multiplied each length by one-half.

Problem C2

Compare the "before" and "after" quadperson when you subtracted half an inch from each length.

Problem C3

Of Problems C1 and C2, which is a relative comparison? Which is an absolute comparison? Explain how you know.

Problem C4

Did the Quadperson look the same after a change made by an absolute comparison? Did the Quadperson look the same after a change made by a relative comparison? Why?

Video SegmentIn this video segment, Andrea and Deanna compare the two versions of Quadperson and discuss why one Quadperson is more in proportion with the original than the other. Watch this segment after you've completed Problems C1-C4, and reflect on the onscreen participants' reasoning about the results of their drawings.

Would every absolute comparison change the shape of Quadperson?
Would every relative comparison maintain the shape of Quadperson?

You can find this segment on the session video, approximately 5 minutes and 58 seconds after the Annenberg Media logo.

Video SegmentIn this video segment, the onscreen participants discover the proportional change in area determined by the relative change in Quadperson.

Can you explain why the two-dimensional area would change in the manner described in this segment? This topic will be further explored in the "Measurement" course.

You can find this segment on the session video, approximately 8 minutes and 41 seconds after the Annenberg Media logo.